Motivation: In biomedicine, every molecular measurement is relative to a reference point, like a fixed aliquot of RNA extracted from a tissue, a defined number of blood cells, or a defined volume of biofluid. Reference points are often chosen for practical reasons. For example, we might want to assess the metabolome of a diseased organ but can only measure metabolites in blood or urine. In this case, the observable data only indirectly reflects the disease state. The statistical implications of these discrepancies in reference points have not yet been discussed. Results: Here, we show that reference point discrepancies compromise the performance of regression models like the LASSO. As an alternative, we suggest zero-sum regression for a reference point insensitive analysis. We show that zero-sum regression is superior to the LASSO in case of a poor choice of reference point both in simulations and in an application that integrates intestinal microbiome analysis with metabolomics. Moreover, we describe a novel coordinate descent based algorithm to fit zero-sum elastic nets.